Seldon user's guide

Sparse complex matrices are structures for which real part and imaginary part are stored independently. The aim is to reduce the required storage when the imaginary part contains much less non-zero entries than the real part. These matrices are not available by default, the file "SeldonComplexMatrix.hxx" (or "SeldonLib.hxx") has to be included in order to use those matrices. Unitary tests are present in the file sparse_complex_matrices.html

Basic declaration of easily modifiable sparse complex matrices:

These matrices are available only after SeldonComplexMatrix.hxx has been included (or SeldonLib.hxx).

Classes :

Matrix<T, Prop, ArrayRowComplexSparse>
Matrix<T, Prop, ArrayColComplexSparse>
Matrix<T, Prop, ArrayRowSymComplexSparse>
Matrix<T, Prop, ArrayColSymComplexSparse>

Example :

#include "SeldonComplexMatrix.hxx"

// sparse complex matrix of doubles
Matrix<complex<double>, General, ArrayRowComplexSparse> A;

// sparse complex symmetric matrix
Matrix<complex<float>, Symmetric, ArrayRowSymComplexSparse> B;

// changing size of the matrix
A.Reallocate(m, n);

// a_13 = a_13 + (1.5,0.7)
A.AddInteraction(1, 3, complex<double>(1.5, 0.7));

Methods for easily modifiable sparse complex matrices :

Matrix constructors
Matrix operators
GetM	returns the number of rows in the matrix
GetN	returns the number of columns in the matrix
GetDataSize	returns the number of elements effectively stored
GetMemorySize	returns the memory used to store the matrix
GetRealDataSize	returns the number of elements effectively stored for the real part
GetImagDataSize	returns the number of elements effectively stored for the imaginary part
GetNonZeros	returns the number of elements effectively stored
GetRealNonZeros	returns the number of elements effectively stored for the real part
GetImagNonZeros	returns the number of elements effectively stored for the imaginary part
GetRealData	returns a pointer to the array containing the values of the real part
GetImagData	returns a pointer to the array containing the values of the imaginary part
GetRealInd	returns a pointer to the array containing the column indexes of the real part
GetImagInd	returns a pointer to the array containing the column indexes of the imaginary part
ValReal	returns a reference to real part of A(i, j)
ValImag	returns a reference to imaginary part of A(i, j)
GetReal	returns a reference to real part of A(i, j)
GetImag	returns a reference to imaginary part of A(i, j)
Set	sets real and imaginary part of A(i, j)
NullifyReal	removes real part of the matrix without releasing memory
NullifyImag	removes imaginary part of the matrix without releasing memory
SetRealData	sets real part of the matrix
SetImagData	sets imaginary part of the matrix
Clear	removes all elements of the matrix
Reallocate	changes the size of matrix (does not keep previous elements)
Resize	changes the size of matrix (keeps previous elements)
ValueReal	direct access to a real value
ValueImag	direct access to an imaginary value
IndexReal	direct access to a column number of real part
IndexImag	direct access to a column number of imaginary part
RemoveSmallEntry	drops small values of the matrix
Zero	sets all elements to zero
SetIdentity	sets matrix to identity matrix
Fill	sets all elements to a given value
FillRand	fills randomly the matrix
ReallocateRealRow / ReallocateRealColumn	changes the size of a row of the real part
ReallocateImagRow / ReallocateImagColumn	changes the size of a row of the imaginary part
ResizeRealRow / ResizeRealColumn	changes the size of a row of real part and keeps previous values
ResizeImagRow / ResizeImagColumn	changes the size of a row of imaginary part and keeps previous values
ClearRealRow / ClearRealColumn	clears a row of real part
ClearImagRow / ClearImagColumn	clears a row of imaginary part
SwapRealRow / SwapRealColumn	exchanges two rows of real part
SwapImagRow / SwapImagColumn	exchanges two rows of imaginary part
ReplaceRealIndexRow / ReplaceRealIndexColumn	changes column numbers of real part
ReplaceImagIndexRow / ReplaceImagIndexColumn	changes column numbers of imaginary part
GetRealRowSize / GetRealColumnSize	returns the number of elements in the row of real part
GetImagRowSize / GetImagColumnSize	returns the number of elements in the row of imaginary part
PrintRealRow / PrintRealColumn	prints a row of real part
PrintImagRow / PrintImagColumn	prints a row of imaginary part
AssembleRealRow / AssembleRealColumn	assembles a row of real part
AssembleImagRow / AssembleImagColumn	assembles a row of imaginary part
AddInteraction	adds/inserts an element in the matrix
AddInteractionRow	adds/inserts an element in a matrix row
AddInteractionColumn	adds/inserts elements in a matrix column
Print	displays the matrix
Write	writes the vector in binary format
Read	reads the vector in binary format
WriteText	writes the vector in text format
ReadText	reads the vector in text format

As for sparse matrices, Harwell-Boeing format can also be used :

Basic declaration of Harwell-Boeing sparse matrices:

Classes :

Matrix<T, Prop, RowComplexSparse>
Matrix<T, Prop, ColComplexSparse>
Matrix<T, Prop, RowSymComplexSparse>
Matrix<T, Prop, ColSymComplexSparse>

Example :

#include "SeldonComplexMatrix.hxx"

// complex sparse matrix of doubles
Matrix<complex<double>, General, RowComplexSparse> A;

// sparse symmetric matrix
Matrix<complex<float>, Symmetric, RowSymComplexSparse> B;

Methods for Harwell-Boeing sparse matrices :

Matrix constructors
Matrix operators
GetM	returns the number of rows in the matrix
GetN	returns the number of columns in the matrix
GetRealDataSize	returns the number of elements effectively stored in the real part
GetImagDataSize	returns the number of elements effectively stored in the imaginary part
GetDataSize	returns the number of elements effectively stored
GetMemorySize	returns the memory used to store the matrix
GetRealNonZeros	returns the number of elements effectively stored in the real part
GetImagNonZeros	returns the number of elements effectively stored in the imaginary part
GetNonZeros	returns the number of elements effectively stored
GetRealData	returns a pointer to the array containing the values of real part
GetImagData	returns a pointer to the array containing the values of imaginary part
GetRealInd	returns a pointer to the array containing column numbers of real part
GetImagInd	returns a pointer to the array containing column numbers of imaginary part
GetRealPtr	returns a pointer to the array containing row numbers of real part
GetImagPtr	returns a pointer to the array containing row numbers of imaginary part
GetRealPtrSize	returns size of array Ptr of real part
GetImagPtrSize	returns size of array Ptr of imaginary part
GetRealIndSize	returns size of array Ind of real part
GetImagIndSize	returns size of array Ind of imaginary part
Clear	removes all elements of the matrix
SetData	sets the pointer to the array containing the values
Nullify	clears the matrix without releasing memory
Reallocate	modifies the size of the matrix
Resize	modifies the size of the matrix
ValReal	direct access to real part of A(i, j)
ValImag	direct access to imaginary part of A(i, j)
GetReal	access to real part of A(i, j)
GetImag	access to imaginary part of A(i, j)
Val	modification of A(i, j)
SetIdentity	initializes the sparse matrix to identity
Fill	fills non-zero entries to a given value
Fill	fills non-zero entries to random values
Print	displays the matrix
Write	writes the vector in binary format
Read	reads the vector in binary format
WriteText	writes the vector in text format
ReadText	reads the vector in text format

Matrix constructors for ArrayRowComplexSparse, ArrayRowSymComplexSparse

Syntax :

  Matrix();
  Matrix(int m, int n);

Example :

// default constructor -> empty matrix
Matrix<complex<double>, General, ArrayRowComplexSparse> V;
cout << "Number of elements "<< V.GetDataSize() << endl; // should return 0 
// then you can use Reallocate to set the number of rows and columns
V.Reallocate(3, 2);
// the last command doesn't create any non-zero element
// you can create one with AddInteraction for example
V.AddInteraction(0, 1, complex<double>(1.5, 0.0) );

// we construct symmetric matrix with 4 rows
Matrix<complex<double>, Symmetric, ArrayRowSymComplexSparse> W(4, 4);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

Matrix constructors for RowComplexSparse, RowSymComplexSparse

Syntax :

  Matrix();
  Matrix(int m, int n);
  Matrix(int m, int n, int real_nnz, int imag_nnz);
  Matrix(m, n, real_values, real_ptr, real_ind, imag_values, imag_ptr, imag_ind);

Example :

// default constructor -> empty matrix
Matrix<complex<double>, General, RowComplexSparse> V;
cout << "Number of elements "<< V.GetDataSize() << endl; // should return 0 

// with this constructor, an empty matrix with 4 rows and columns is constructed
Matrix<complex<double>, Symmetric, RowSymComplexSparse> W(4, 4);

// Here a matrix with 3 rows, 4 columns and 10 non-zero entries
// for the real part, and 2 non-zero entries for imaginary part
// however non-zero entries are not initialized, you can
// set them by modifying arrays returned by GetRealPtr(), GetRealInd(), GetRealData()
Matrix<complex<double>, General, RowComplexSparse> A(3, 4, 10, 2);

// in the last constructor you provide
int m = 5; // number of rows
int n = 6; // number of columns
int real_nnz = 12; // number of non-zero entries for real part
int imag_nnz = 4; // number of non-zero entries for imaginary part
Vector<double> real_values(real_nnz), imag_values(imag_nnz); // values
real_values.FillRand(); // you have to initialize values
imag_values.FillRand(); // you have to initialize values
Vector<int> real_col(real_nnz), imag_col(imag_nnz); // for each value column number
// for each row, column numbers are sorted
// first row
real_col(0) = 0;
real_col(1) = 2;
real_col(2) = 4;
// second row
real_col(3) = 1;
imag_col(0) = 2;
// third row
real_col(4) = 0;
real_col(5) = 1;
real_col(6) = 3;
imag_col(1) = 0;
imag_col(2) = 3;
// fourth row
real_col(7) = 4;
real_col(8) = 5;
// last row
real_col(9) = 2;
real_col(10) = 3;
real_col(11) = 5;
imag_col(3) = 4;
// for each row, index of first value
Vector<int> real_ptr(m+1), imag_ptr(m+1); 
real_ptr(0) = 0;
real_ptr(1) = 3;
real_ptr(2) = 4;
real_ptr(3) = 7;
real_ptr(4) = 9;
real_ptr(5) = 12;
imag_ptr(0) = 0;
imag_ptr(1) = 0;
imag_ptr(2) = 1;
imag_ptr(3) = 3;
imag_ptr(4) = 3;
imag_ptr(5) = 4;
// values on the row are to be seeked between xx_ptr(i) and xx_ptr(i+1)

// Now the constructor:
Matrix<complex<double>, General, RowComplexSparse> M(m, n, real_values, real_ptr, real_col, imag_values, imag_ptr, imag_col);
// Note that 'values', 'ptr' and 'columns' are nullified (that is, emptied):
// the arrays to which they pointed have been transferred to M.

Location :

Class Matrix_ComplexSparse
Class Matrix_SymComplexSparse
Matrix_ComplexSparse.hxx Matrix_ComplexSparse.cxx
Matrix_SymComplexSparse.hxx Matrix_SymComplexSparse.cxx

Matrix operators

Syntax :

  const T& operator (int i, int j) const;
  Matrix& operator =(const T0& alpha)

The operator () cannot be used to insert or modify elements of matrix. Use rather the methods GetReal or ValReal for the real part, and corresponding methods for the imaginary part.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(3, 3);
// use of operator () to know the value of A(i, j);
cout << V(2, 0) << endl;

// set all elements to a given value
V = 1;

Location :

Class Matrix_ArrayComplexSparse
Class Matrix_ComplexSparse
Class Matrix_SymComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx
Matrix_ComplexSparse.hxx Matrix_ComplexSparse.cxx
Matrix_SymComplexSparse.hxx Matrix_SymComplexSparse.cxx

GetM

Syntax :

  int GetM() const

This method returns the numbers of rows of the matrix.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(4, 3);
// GetM() should return 4
cout << "Number of rows of V : " << V.GetM() << endl;

Location :

GetN

Syntax :

  int GetN() const

This method returns the numbers of columns of the matrix.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(4, 3);
// GetN() should return 3
cout << "Number of columns of V : " << V.GetN() << endl;

Location :

GetDataSize, GetNonZeros

Syntax :

  int GetDataSize() const
  int GetNonZeros() const

This method returns the elements effectively stored in the matrix.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(4, 3);
// GetDataSize() should return 0
cout << "Number of elements in V : " << V.GetDataSize() << endl;
// then we add some values
V.AddInteraction(0, 2, complex<double>(1.0, 0));
V.AddInteraction(1, 0, complex<double>(0, 0.3));
V.AddInteraction(3, 1, complex<double>(2.3, 0));
V.AddInteraction(2, 0, complex<double>(-0.5, 0.8));
V.AddInteraction(2, 2, complex<double>(1.2, 0));
// GetDataSize should return 6 (four element in real part, two in imaginary part)
cout << "Number of elements in V : " << V.GetDataSize() << endl;

Location :

GetMemorySize

Syntax :

  size_t GetMemorySize() const

This method returns the memory used to store the matrix in bytes.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(4, 3);
// GetDataSize() should return 0
cout << "Number of elements in V : " << V.GetDataSize() << endl;
// then we add some values
V.AddInteraction(0, 2, complex<double>(1.0, 0));
V.AddInteraction(1, 0, complex<double>(0, 0.3));
V.AddInteraction(3, 1, complex<double>(2.3, 0));
V.AddInteraction(2, 0, complex<double>(-0.5, 0.8));
V.AddInteraction(2, 2, complex<double>(1.2, 0));
// GetMemorySize returns the memory used to store V (in bytes)
cout << "Memory used to store V : " << V.GetMemorySize() << endl;

Location :

GetRealDataSize,GetRealNonZeros

Syntax :

  int GetRealDataSize() const
  int GetRealNonZeros() const

This method returns the elements effectively stored in the real part of the matrix.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(4, 3);
// GetRealDataSize() should return 0
cout << "Number of elements in V : " << V.GetRealDataSize() << endl;
// then we add some values
V.AddInteraction(0, 2, complex<double>(1.0, 0));
V.AddInteraction(1, 0, complex<double>(0, 0.3));
V.AddInteraction(3, 1, complex<double>(2.3, 0));
V.AddInteraction(2, 0, complex<double>(-0.5, 0.8));
V.AddInteraction(2, 2, complex<double>(1.2, 0));
// GetRealDataSize should return 4
cout << "Number of elements in V : " << V.GetRealDataSize() << endl;

Location :

GetImagDataSize, GetImagNonZeros

Syntax :

  int GetImagDataSize() const
  int GetImagNonZeros() const

This method returns the elements effectively stored in the imaginary part of the matrix.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(4, 3);
// GetImagDataSize() should return 0
cout << "Number of elements in V : " << V.GetImagDataSize() << endl;
// then we add some values
V.AddInteraction(0, 2, complex<double>(1.0, 0));
V.AddInteraction(1, 0, complex<double>(0, 0.3));
V.AddInteraction(3, 1, complex<double>(2.3, 0));
V.AddInteraction(2, 0, complex<double>(-0.5, 0.8));
V.AddInteraction(2, 2, complex<double>(1.2, 0));
// GetImagDataSize should return 2
cout << "Number of elements in V : " << V.GetImagDataSize() << endl;

Location :

GetRealData for ArrayRowComplexSparse, ArrayRowSymComplexSparse

Syntax :

  T* GetRealData(int i) const
  Vector<T, VectSparse>* GetRealData() const

This method returns a pointer to the values stored in the row i, or if no argument is provided, it returns the pointer to the vector of sparse vectors (each sparse vector is a row of the real part of the matrix).

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// if you want to have a C-array with real values of second row :
double* data = A.GetRealData(1);
// size of this array
int size_row = A.GetRealRowSize(1);
// for example we sum real parts
double sum = 0;
for (int i = 0; i < size_row; i++)
  sum += data[i];

// if you want a pointer to all the real part
Vector<double, VectSparse>* ptr = A.GetRealData();
// size of this array is the number of rows
for (int i = 0; i < A.GetM(); i++)
    cout << "Number of elements in real part of row " << i << " : " << ptr[i].GetM() << endl;

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

GetImagData for ArrayRowComplexSparse, ArrayRowSymComplexSparse

Syntax :

  T* GetImagData(int i) const
  Vector<T, VectSparse>* GetImagData() const

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// if you want to have a C-array with imaginary values of third row :
double* data = A.GetImagData(2);
// size of this array
int size_row = A.GetImagRowSize(2);
// for example we sum imaginary parts
double sum = 0;
for (int i = 0; i < size_row; i++)
  sum += data[i];

// if you want a pointer to all the imaginary part
Vector<double, VectSparse>* ptr = A.GetImagData();
// size of this array is the number of rows
for (int i = 0; i < A.GetM(); i++)
    cout << "Number of elements in imaginary part of row " << i << " : " << ptr[i].GetM() << endl;

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

GetRealData for RowComplexSparse, RowSymComplexSparse

Syntax :

  T* GetRealData() const

This method returns a pointer to the values stored in the matrix (only real part).

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// if you want to have a C-array with real values of the matrix :
double* data = A.GetRealData();
// size of this array
int size_data = A.GetRealDataSize(1);
// for example we sum all the non-zero entries
double sum = 0;
for (int i = 0; i < size_data; i++)
  sum += data[i];

Location :

Class Matrix_ComplexSparse
Class Matrix_SymComplexSparse
Matrix_ComplexSparse.hxx Matrix_ComplexSparse.cxx
Matrix_SymComplexSparse.hxx Matrix_SymComplexSparse.cxx

GetImagData for RowComplexSparse, RowSymComplexSparse

Syntax :

  T* GetImagData() const

This method returns a pointer to the values stored in the matrix (only imaginary part).

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// if you want to have a C-array with imaginary values of the matrix :
double* data = A.GetImagData();
// size of this array
int size_data = A.GetImagDataSize(1);
// for example we sum all the non-zero entries
double sum = 0;
for (int i = 0; i < size_data; i++)
  sum += data[i];

Location :

Class Matrix_ComplexSparse
Class Matrix_SymComplexSparse
Matrix_ComplexSparse.hxx Matrix_ComplexSparse.cxx
Matrix_SymComplexSparse.hxx Matrix_SymComplexSparse.cxx

GetRealInd for RowComplexSparse, RowSymComplexSparse

Syntax :

  int* GetRealInd() const

This method returns a pointer to the column numbers of the matrix (only real part).

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// if you want to have a C-array with columns numbers of the real part of matrix :
int* ind = A.GetRealInd();
// we retrieve values and offsets as well
double* data = A.GetRealInd();
int* ptr = A.GetRealPtr();
// for example we sum all the non-zero entries not on the diagonal
double sum = 0;
for (int i = 0; i < A.GetM(); i++)
  for (int j = ptr[i]; j < ptr[i+1]; j++)
    if (ind[j] != i)
      sum += data[i];

Location :

Class Matrix_ComplexSparse
Class Matrix_SymComplexSparse
Matrix_ComplexSparse.hxx Matrix_ComplexSparse.cxx
Matrix_SymComplexSparse.hxx Matrix_SymComplexSparse.cxx

GetImagInd for RowComplexSparse, RowSymComplexSparse

Syntax :

  int* GetImagInd() const

This method returns a pointer to the column numbers of the matrix (only imaginary part).

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// if you want to have a C-array with columns numbers of the imaginary part of matrix :
int* ind = A.GetImagInd();
// we retrieve values and offsets as well
double* data = A.GetImagInd();
int* ptr = A.GetImagPtr();
// for example we sum all the non-zero entries not on the diagonal
double sum = 0;
for (int i = 0; i < A.GetM(); i++)
  for (int j = ptr[i]; j < ptr[i+1]; j++)
    if (ind[j] != i)
      sum += data[i];

Location :

Class Matrix_ComplexSparse
Class Matrix_SymComplexSparse
Matrix_ComplexSparse.hxx Matrix_ComplexSparse.cxx
Matrix_SymComplexSparse.hxx Matrix_SymComplexSparse.cxx

GetRealPtr for RowComplexSparse, RowSymComplexSparse

Syntax :

  int* GetRealPtr() const

This method returns a pointer to the array containing starting indices of rows (only real part).

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// if you want to have a C-array with columns numbers of the real part of matrix :
int* ind = A.GetRealInd();
// we retrieve values and offsets as well
double* data = A.GetRealInd();
int* ptr = A.GetRealPtr();
// for example we sum all the non-zero entries not on the diagonal
double sum = 0;
for (int i = 0; i < A.GetM(); i++)
  for (int j = ptr[i]; j < ptr[i+1]; j++)
    if (ind[j] != i)
      sum += data[i];

Location :

Class Matrix_ComplexSparse
Class Matrix_SymComplexSparse
Matrix_ComplexSparse.hxx Matrix_ComplexSparse.cxx
Matrix_SymComplexSparse.hxx Matrix_SymComplexSparse.cxx

GetImagPtr for RowComplexSparse, RowSymComplexSparse

Syntax :

  int* GetImagPtr() const

This method returns a pointer to the array containing starting indices of rows (only imaginary part).

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// if you want to have a C-array with columns numbers of the imaginary part of matrix :
int* ind = A.GetImagInd();
// we retrieve values and offsets as well
double* data = A.GetImagInd();
int* ptr = A.GetImagPtr();
// for example we sum all the non-zero entries not on the diagonal
double sum = 0;
for (int i = 0; i < A.GetM(); i++)
  for (int j = ptr[i]; j < ptr[i+1]; j++)
    if (ind[j] != i)
      sum += data[i];

Location :

Class Matrix_ComplexSparse
Class Matrix_SymComplexSparse
Matrix_ComplexSparse.hxx Matrix_ComplexSparse.cxx
Matrix_SymComplexSparse.hxx Matrix_SymComplexSparse.cxx

SetData for RowComplexSparse, RowSymComplexSparse

Syntax :

  void SetData(int m, int n, int real_nz, T* real_data, int* real_ptr, int* real_ind, T* imag_data, int* imag_ptr, int* imag_ind);
  void SetData(int m, int n, Vector<T> real_data, Vector<int> real_ptr, Vector<int> real_ind,
                             Vector<T> imag_data, Vector<int> imag_ptr, Vector<int> imag_ind)

This method initializes directly the matrix by providing the arrays Ptr, Ind and Data.

Example :

int m = 5; // number of rows
int n = 6; // number of columns
int real_nnz = 12; // number of non-zero entries for real part
int imag_nnz = 4; // number of non-zero entries for imaginary part
Vector<double> real_values(real_nnz), imag_values(imag_nnz); // values
real_values.FillRand(); // you have to initialize values
imag_values.FillRand(); // you have to initialize values
Vector<int> real_col(real_nnz), imag_col(imag_nnz); // for each value column number
// for each row, column numbers are sorted
// first row
real_col(0) = 0;
real_col(1) = 2;
real_col(2) = 4;
// second row
real_col(3) = 1;
imag_col(0) = 2;
// third row
real_col(4) = 0;
real_col(5) = 1;
real_col(6) = 3;
imag_col(1) = 0;
imag_col(2) = 3;
// fourth row
real_col(7) = 4;
real_col(8) = 5;
// last row
real_col(9) = 2;
real_col(10) = 3;
real_col(11) = 5;
imag_col(3) = 4;
// for each row, index of first value
Vector<int> real_ptr(m+1), imag_ptr(m+1); 
real_ptr(0) = 0;
real_ptr(1) = 3;
real_ptr(2) = 4;
real_ptr(3) = 7;
real_ptr(4) = 9;
real_ptr(5) = 12;
imag_ptr(0) = 0;
imag_ptr(1) = 0;
imag_ptr(2) = 1;
imag_ptr(3) = 3;
imag_ptr(4) = 3;
imag_ptr(5) = 4;
// values on the row are to be seeked between xx_ptr(i) and xx_ptr(i+1)

Matrix<complex<double>, General, RowComplexSparse> A;

// Initialisation of A
A.SetData(m, n, real_values, real_ptr, real_col, imag_values, imag_ptr, imag_col);
// Note that 'values', 'ptr' and 'columns' are nullified (that is, emptied):
// the arrays to which they pointed have been transferred to M.

Location :

Class Matrix_ComplexSparse
Class Matrix_SymComplexSparse
Matrix_ComplexSparse.hxx Matrix_ComplexSparse.cxx
Matrix_SymComplexSparse.hxx Matrix_SymComplexSparse.cxx

Nullify for RowComplexSparse, RowSymComplexSparse

Syntax :

  void Nullify()

This method nullifies pointer without releasing the memory. On output, the matrix is 0x0 with 0 non-zero entries.

Example :

// reading A from a file
Matrix<complex<double>, General, RowComplexSparse> A;
A.ReadText("mat.dat");

// then retrieving C-pointers
int  m = A.GetM();
int nnz = A.GetDataSize();
int* ptr = A.GetPtr();
int* ind = A.GetInd();
double* data = A.GetData();

// if you wish to handle deallocation of these pointers by your-self :
A.Nullify();

Location :

Class Matrix_ComplexSparse
Class Matrix_SymComplexSparse
Matrix_ComplexSparse.hxx Matrix_ComplexSparse.cxx
Matrix_SymComplexSparse.hxx Matrix_SymComplexSparse.cxx

GetRealInd for ArrayRowComplexSparse, ArrayRowSymComplexSparse

Syntax :

  int* GetRealInd(int i) const

This method returns a pointer to the column numbers of the real part of sparse row i.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// if you want to have a C-array with real values of second row :
double* data = A.GetRealData(1);
// and wish the column indexes as well
int* col = A.GetRealInd(1);
// size of this array
int size_row = A.GetRealRowSize(1);
// for example we sum real parts except diagonal
double sum = 0;
for (int i = 0; i < size_row; i++)
  if (col[i] != 1)
    sum += data[i];

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

GetImagInd for ArrayRowComplexSparse, ArrayRowSymComplexSparse

Syntax :

  int* GetImagInd(int i) const

This method returns a pointer to the column numbers of the imaginary part of sparse row i.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// if you want to have a C-array with imaginary values of third row :
double* data = A.GetImagData(2);
// and column indexes :
int* col = A.GetImagInd(2);
// size of this array
int size_row = A.GetImagRowSize(2);
// for example we sum imaginary parts except on diagonal
double sum = 0;
for (int i = 0; i < size_row; i++)
  if (col[i] != 2)
    sum += data[i];

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

ValReal

Syntax :

  T& ValReal(int i, int j)

This method returns a reference to real part of A(i, j) so that you can modify directly the matrix. If the position (i, j) does not correspond to a non-zero entry, an exception is raised (in debug mode). This method does not create new non-zero entries, use rather GetReal to this aim.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(10, 4);
// in a first step, you fill the matrix
A.GetReal(0, 3) = 2.0;
A.GetImag(0, 2) = 1.5;
A.GetReal(1, 1) = -2.3;
A.GetImag(1, 1) = 0.2;
// then you can modify the real part with ValReal
A.ValReal(0, 3) = 1.0;
// next line should raise an exception
A.ValReal(2, 3) = 0.2;

Location :

ValImag

Syntax :

  T& ValImag(int i, int j)

This method returns a reference to imaginary part of A(i, j) so that you can modify directly the matrix. If the position (i, j) does not correspond to a non-zero entry, an exception is raised (in debug mode). This method does not create new non-zero entries, use rather GetImag to this aim.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(10, 4);
// in a first step, you fill the matrix
A.GetReal(0, 3) = 2.0;
A.GetImag(0, 2) = 1.5;
A.GetReal(1, 1) = -2.3;
A.GetImag(1, 1) = 0.2;
// then you can modify the imaginary part with ValImag
A.ValImag(0, 2) = 1.0;
// next line should raise an exception
A.ValImag(2, 3) = 0.2;

Location :

GetReal

Syntax :

  T& GetReal(int i, int j)

This method returns a reference to real part of A(i, j) so that you can modify directly the matrix. If the position (i, j) does not correspond to a non-zero entry, a new non-zero entry is created.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(10, 4);
// you can fill the matrix with GetReal/GetImag
A.GetReal(0, 3) = 2.0;
A.GetImag(0, 2) = 1.5;
A.GetReal(1, 1) = -2.3;
A.GetImag(1, 1) = 0.2;

Location :

GetImag

Syntax :

  T& GetImag(int i, int j)

This method returns a reference to imaginary part of A(i, j) so that you can modify directly the matrix. If the position (i, j) does not correspond to a non-zero entry, a new non-zero entry is created.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(10, 4);
// you can fill the matrix with GetReal/GetImag
A.GetReal(0, 3) = 2.0;
A.GetImag(0, 2) = 1.5;
A.GetReal(1, 1) = -2.3;
A.GetImag(1, 1) = 0.2;
A.ValImag(2, 3) = 0.2;

Location :

Set

Syntax :

  void Set(int i, int j, const complex<T>& val);

This method sets real and imaginary part A(i, j) so that you can modify directly the matrix. If the position (i, j) does not correspond to a non-zero entry, a new non-zero entry is created.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(10, 4);
// you can fill the matrix with Set
A.Set(0, 3, complex<double>(2.0, -0.5));
A.Set(0, 2, complex<double>(1.5, 0.2));
A.Set(1, 1, complex<double>(-2.3, 0));
A.Set(2, 3, complex<double>(0, 0.2));

Location :

NullifyReal

Syntax :

  void NullifyReal(int i)
  void NullifyReal()

This method empties a single row of the matrix or the entire matrix (only real part) without releasing the memory. It should be used carefully and usually in conjunction with SetRealData.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// if you want to have a C-array with real values of second row :
double* data = A.GetRealData(1);
// and column indexes
int* col = A.GetRealInd(1);
// size of this array
int size_row = A.GetRealRowSize(1);
// you can initialize a sparse vector with those pointers
Vector<double, VectSparse> single_row;
single_row.SetData(size_row, data, col);
// then to avoid multiple deallocations, NullifyReal is useful :
A.NullifyReal(1);

// if you want a pointer to all the real part
Vector<double, VectSparse>* ptr = A.GetRealData();
int m = A.GetM();
// and nullify all the real part
A.NullifyReal();

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

NullifyImag

Syntax :

  void NullifyImag(int i)
  void NullifyImag()

This method empties a single row of the matrix or the entire matrix (only imaginary part) without releasing the memory. It should be used carefully and usually in conjunction with SetImagData.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// if you want to have a C-array with imaginary values of second row :
double* data = A.GetImagData(1);
// and column indexes
int* col = A.GetImagInd(1);
// size of this array
int size_row = A.GetImagRowSize(1);
// you can initialize a sparse vector with those pointers
Vector<double, VectSparse> single_row;
single_row.SetData(size_row, data, col);
// then to avoid multiple deallocations, NullifyImag is useful :
A.NullifyImag(1);

// if you want a pointer to all the imaginary part
Vector<double, VectSparse>* ptr = A.GetImagData();
int m = A.GetM();
// and nullify all the imaginary part
A.NullifyImag();

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

SetRealData

Syntax :

  void SetRealData(int m, int n, Vector<T, VectSparse>* real_part)
  void SetRealData(int i, int size_row, T* val, int* col);

With this method, you can set directly the pointers containing the real part of a single row, or the real part of the entire matrix. This low-level method should be used cautiously.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 6);
// you initialize values and column numbers of a row
int size_row = 3;
Vector<double> values(size_row); Vector<int> cols(size_row);
values(0) = 1.3; cols(0) = 0;
values(1) = -3.5; cols(1) = 2;
values(2) = 5.2; cols(2) = 5;
// then you initialize a row with these datas
int irow = 2;
A.SetRealData(irow, size_row, values.GetData(), cols.GetData());
// nullify values and cols to avoid multiple deallocations
values.Nullify(); cols.Nullify();

// you can also construct all the rows of real part
int m = 4, n = 6;
Vector<Vector<double, VectSparse> > all_rows(m);
all_rows(0).Get(1) = 2.3;
all_rows(0).Get(3) = 1.8;
all_rows(1).Get(1) = -0.3;
all_rows(2).Get(5) = 9.1;
all_rows(2).Get(2) = 0.2;
all_rows(3).Get(4) = 0.9;
// and feed the real part of the matrix with all_rows
A.SetRealData(m, n, all_rows.GetData());
// nullify all_rows to avoid multiple deallocations
all_rows.Nullify();

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

SetImagData

Syntax :

  void SetImagData(int m, int n, Vector<T, VectSparse>* real_part)
  void SetImagData(int i, int size_row, T* val, int* col);

With this method, you can set directly the pointers containing the imaginary part of a single row, or the real part of the entire matrix. This low-level method should be used cautiously.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 6);
// you initialize values and column numbers of a row
int size_row = 3;
Vector<double> values(size_row); Vector<int> cols(size_row);
values(0) = 1.3; cols(0) = 0;
values(1) = -3.5; cols(1) = 2;
values(2) = 5.2; cols(2) = 5;
// then you initialize a row with these datas
int irow = 2;
A.SetImagData(irow, size_row, values.GetData(), cols.GetData());
// nullify values and cols to avoid multiple deallocations
values.Nullify(); cols.Nullify();

// you can also construct all the rows of imaginary part
int m = 4, n = 6;
Vector<Vector<double, VectSparse> > all_rows(m);
all_rows(0).Get(1) = 2.3;
all_rows(0).Get(3) = 1.8;
all_rows(1).Get(1) = -0.3;
all_rows(2).Get(5) = 9.1;
all_rows(2).Get(2) = 0.2;
all_rows(3).Get(4) = 0.9;
// and feed the imaginary part of the matrix with all_rows
A.SetImagData(m, n, all_rows.GetData());
// nullify all_rows to avoid multiple deallocations
all_rows.Nullify();

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

Clear

Syntax :

  void Clear()

This method clears the matrix. On output, the matrix is 0x0 with 0 non-zero entries.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(4, 3);
// GetM() should return 4
cout << "Number of rows of V : " << V.GetM() << endl;

// the matrix is cleared
V.Clear();
// GetM() should return 0
cout << "Number of rows of V : " << V.GetM() << endl;

Location :

Reallocate

Syntax :

  void Reallocate(int m, int n)

This method reallocates the matrix, previous non-zero entries are removed (you don't need to call Clear).

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(4, 3);
// GetM() should return 4
cout << "Number of rows of V : " << V.GetM() << endl;

// the matrix is reallocated
// new matrix will contain 0 non-zero entries
V.Reallocate(6, 10);
cout << "Number of rows of V : " << V.GetM() << endl;

Location :

Resize

Syntax :

  void Resize(int m, int n)

This method resizes the matrix, previous non-zero entries are kept if they are always in the scope of the matrix (if you reduce the numbers of rows or columns of the matrix, some non-zero entries will be removed).

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(4, 3);
// filling the matrix
A.Set(1, 2, complex<double>(0.3, 1.5));
A.Set(0, 3, complex<double>(0, 1.8));
A.Set(0, 0, complex<double>(2.3, 0));
A.Set(2, 1, complex<double>(-1.1, 0.7));

// the matrix is resized
// new matrix will contain the previous non-zero entries
V.Resize(6, 10);
cout << "Number of non-zero entries of V : " << V.GetDataSize() << endl;

Location :

ValueReal

Syntax :

  T ValueReal(int i, int j)

This method returns the j-th non-zero entry of real part of i-th row. It can be used to fill directly the matrix with IndexReal, and ReallocateRealRow.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(4, 3);
// filling the real part with IndexReal, ValueReal
A.ReallocateRealRow(0, 2);
A.IndexReal(0, 0) = 3;
A.ValueReal(0, 0) = 1.8;
A.IndexReal(0, 1) = 0;
A.ValueReal(0, 1) = 2.3;
// for row 0, the column indexes are not sorted -> call AssembleRealRow
A.AssembleRealRow(0);
// or provide sorted column indexes
A.ReallocateRealRow(1, 1);
A.IndexReal(1, 0) = 2;
A.ValueReal(1, 0) = 0.3;
A.ReallocateRealRow(2, 1);
A.IndexReal(2, 0) = 1;
A.ValueReal(2, 0) = -1.1;

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

ValueImag

Syntax :

  T ValueImag(int i, int j)

This method returns the j-th non-zero entry of imaginary part of i-th row. It can be used to fill directly the matrix with IndexImag, and ReallocateImagRow.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(4, 3);
// filling the imaginary part with IndexImag, ValueImag
A.ReallocateImagRow(0, 2);
A.IndexImag(0, 0) = 3;
A.ValueImag(0, 0) = 1.8;
A.IndexImag(0, 1) = 0;
A.ValueImag(0, 1) = 2.3;
// for row 0, the column indexes are not sorted -> call AssembleImagRow
A.AssembleImagRow(0);
// or provide sorted column indexes
A.ReallocateImagRow(1, 1);
A.IndexImag(1, 0) = 2;
A.ValueImag(1, 0) = 0.3;
A.ReallocateImagRow(2, 1);
A.IndexImag(2, 0) = 1;
A.ValueImag(2, 0) = -1.1;

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

IndexReal

Syntax :

  int IndexReal(int i, int j)

This method returns the column index of j-th non-zero entry of real part of i-th row. It can be used to fill directly the matrix with ValueReal, and ReallocateRealRow.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(4, 3);
// filling the real part with IndexReal, ValueReal
A.ReallocateRealRow(0, 2);
A.IndexReal(0, 0) = 3;
A.ValueReal(0, 0) = 1.8;
A.IndexReal(0, 1) = 0;
A.ValueReal(0, 1) = 2.3;
// for row 0, the column indexes are not sorted -> call AssembleRealRow
A.AssembleRealRow(0);
// or provide sorted column indexes
A.ReallocateRealRow(1, 1);
A.IndexReal(1, 0) = 2;
A.ValueReal(1, 0) = 0.3;
A.ReallocateRealRow(2, 1);
A.IndexReal(2, 0) = 1;
A.ValueReal(2, 0) = -1.1;

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

IndexImag

Syntax :

  T IndexImag(int i, int j)

This method returns the column number of j-th non-zero entry of imaginary part of i-th row. It can be used to fill directly the matrix with ValueImag, and ReallocateImagRow.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> V(4, 3);
// filling the imaginary part with IndexImag, ValueImag
A.ReallocateImagRow(0, 2);
A.IndexImag(0, 0) = 3;
A.ValueImag(0, 0) = 1.8;
A.IndexImag(0, 1) = 0;
A.ValueImag(0, 1) = 2.3;
// for row 0, the column indexes are not sorted -> call AssembleImagRow
A.AssembleImagRow(0);
// or provide sorted column indexes
A.ReallocateImagRow(1, 1);
A.IndexImag(1, 0) = 2;
A.ValueImag(1, 0) = 0.3;
A.ReallocateImagRow(2, 1);
A.IndexImag(2, 0) = 1;
A.ValueImag(2, 0) = -1.1;

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

RemoveSmallEntry

Syntax :

  void RemoveSmallEntry(T epsilon)

This method drops non-zero entries which are smaller than a given epsilon.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// you fill the matrix A

// then you can remove small non-zero entries
// i.e values such that |Re(A(i, j))| < epsilon and 
// |Im(A(i, j))| < epsilon are removed
A.RemoveSmallEntry(1e-3);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

Zero

Syntax :

  void Zero();

This method sets the value of non-zero entries to 0. It may be useful if you want to keep the pattern of a matrix and reset the values.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
// you fill the matrix A
A.GetReal(1, 3) = 2.5;
A.GetImag(2, 4) = -0.6;
// ...

// then you can zero non-zero entries
A.Zero();
// and modify values of the pattern
A.ValReal(1, 3) = 0.8;

Location :

SetIdentity

Syntax :

  void SetIdentity();

This method forms the identity matrix.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(10, 10);
// you can initialize A with identity
A.SetIdentity();

Location :

Fill

Syntax :

  void Fill();
  void Fill(T val);

This method sets values of non-zero entries to 0, 1, 2, 3, etc or with a given value val. The sparsity pattern of the matrix keeps unchanged.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(10, 10);
// fill the matrix A
A.GetReal(0, 2) = 1.4;
A.GetReal(0, 1) = 0.5;
A.GetReal(1, 7) = -2.1;
A.GetReal(2, 3) = 1.7;
A.GetImag(2, 3) = 0.9;
A.GetImag(3, 5) = -3.3;

// then you can put the same value on all non-zero entries :
A.Fill(complex<double>(2.0, 1.0));
// A will be equal to 
// 0 1  (2.0, 0)
// 0 2  (2.0, 0)
// 1 7  (2.0, 0)
// 2 3  (2.0, 1.0)
// 3 5  (0.0, 1.0)

// if you call Fill without argument, there will be 0, 1, 2, ...
A.Fill();
// A will be equal to 
// 0 1 (0, 0)
// 0 2  (1, 0)
// 1 7  (2, 0)
// 2 3  (3, 4)
// 3 5  (0, 5)

Location :

FillRand

Syntax :

  void FillRand();

This method sets randomly values of non-zero entries, the profile of the matrix is not modified.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(10, 10);
// fill the matrix A
A.GetReal(0, 2) = 1.4;
A.GetReal(0, 1) = 0.5;
A.GetReal(1, 7) = -2.1;
A.GetReal(2, 3) = 1.7;
A.GetImag(2, 3) = 0.9;
A.GetImag(3, 5) = -3.3;

// then you can put random values on non-zero entries
A.FillRand();
// A will be equal to 
// 0 1  (x0, 0)
// 0 2  (x1, 0)
// 1 7  (x2, 0)
// 2 3  (x3, x4)
// 3 5  (0.0, x5)
// where x0, x1, x2, x3, x4, x5 are random numbers

Location :

ReallocateRealRow

Syntax :

  void ReallocateRealRow(int i, int size_row)

This method modifies the number of non-zero entries contained in real part of row i. All non-zero entries of the real part of the row are resetted, you need to initialize them with IndexReal, ValueReal.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateRealRow(0, 3);
A.IndexReal(0, 0) = 0; A.ValueReal(0, 0) = 2.3;
A.IndexReal(0, 1) = 3; A.ValueReal(0, 1) = -0.8;
A.IndexReal(0, 2) = 7; A.ValueReal(0, 2) = 1.9;
// row 1 with 4 non-zero entries
A.ReallocateRealRow(1, 4);
A.IndexReal(1, 0) = 5; A.ValueReal(1, 0) = 3.1;
A.IndexReal(1, 1) = 1; A.ValueReal(1, 1) = -1.3;
A.IndexReal(1, 2) = 0; A.ValueReal(1, 2) = 2.4;
A.IndexReal(1, 3) = 2; A.ValueReal(1, 3) = 0.4;
// column numbers are not sorted -> AssembleRealRow
A.AssembleRealRow(1);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

ReallocateImagRow

Syntax :

  void ReallocateImagRow(int i, int size_row)

This method modifies the number of non-zero entries contained in imaginary part of row i. All non-zero entries of the imaginary part of the row are resetted, you need to initialize them with IndexImag, ValueImag.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateImagRow(0, 3);
A.IndexImag(0, 0) = 0; A.ValueImag(0, 0) = 2.3;
A.IndexImag(0, 1) = 3; A.ValueImag(0, 1) = -0.8;
A.IndexImag(0, 2) = 7; A.ValueImag(0, 2) = 1.9;
// row 1 with 4 non-zero entries
A.ReallocateImagRow(1, 4);
A.IndexImag(1, 0) = 5; A.ValueImag(1, 0) = 3.1;
A.IndexImag(1, 1) = 1; A.ValueImag(1, 1) = -1.3;
A.IndexImag(1, 2) = 0; A.ValueImag(1, 2) = 2.4;
A.IndexImag(1, 3) = 2; A.ValueImag(1, 3) = 0.4;
// column numbers are not sorted -> AssembleImagRow
A.AssembleImagRow(1);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

ResizeRealRow

Syntax :

  void ResizeRealRow(int i, int size_row)

This method modifies the number of non-zero entries contained in real part of row i. Previous non-zero entries of the real part of the row are kept. If there are new non-zero entries, you need to initialize them with IndexReal, ValueReal.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateRealRow(0, 3);
A.IndexReal(0, 0) = 0; A.ValueReal(0, 0) = 2.3;
A.IndexReal(0, 1) = 3; A.ValueReal(0, 1) = -0.8;
A.IndexReal(0, 2) = 7; A.ValueReal(0, 2) = 1.9;
// row 1 with 4 non-zero entries
A.ReallocateRealRow(1, 4);
A.IndexReal(1, 0) = 5; A.ValueReal(1, 0) = 3.1;
A.IndexReal(1, 1) = 1; A.ValueReal(1, 1) = -1.3;
A.IndexReal(1, 2) = 0; A.ValueReal(1, 2) = 2.4;
A.IndexReal(1, 3) = 2; A.ValueReal(1, 3) = 0.4;
// column numbers are not sorted -> AssembleRealRow
A.AssembleRealRow(1);

// adding a new zero-entry in row 0 :
A.ResizeRealRow(0, 4);
A.IndexReal(0, 3) = 4; A.ValueReal(0, 3) = 4.5;
// column numbers are not sorted -> Assemble
A.AssembleRealRow(0);

// removing last non-zero entry in row (col 5 value 3.1)
A.ResizeRealRow(1, 3);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

ResizeImagRow

Syntax :

  void ResizeImagRow(int i, int size_row)

This method modifies the number of non-zero entries contained in imaginary part of row i. Previous non-zero entries of the imaginary part of the row are kept. If there are new non-zero entries, you need to initialize them with IndexImag, ValueImag.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateImagRow(0, 3);
A.IndexImag(0, 0) = 0; A.ValueImag(0, 0) = 2.3;
A.IndexImag(0, 1) = 3; A.ValueImag(0, 1) = -0.8;
A.IndexImag(0, 2) = 7; A.ValueImag(0, 2) = 1.9;
// row 1 with 4 non-zero entries
A.ReallocateImagRow(1, 4);
A.IndexImag(1, 0) = 5; A.ValueImag(1, 0) = 3.1;
A.IndexImag(1, 1) = 1; A.ValueImag(1, 1) = -1.3;
A.IndexImag(1, 2) = 0; A.ValueImag(1, 2) = 2.4;
A.IndexImag(1, 3) = 2; A.ValueImag(1, 3) = 0.4;
// column numbers are not sorted -> AssembleImagRow
A.AssembleImagRow(1);

// adding a new zero-entry in row 0 :
A.ResizeImagRow(0, 4);
A.IndexImag(0, 3) = 4; A.ValueImag(0, 3) = 4.5;
// column numbers are not sorted -> Assemble
A.AssembleImagRow(0);

// removing last non-zero entry in row (col 5 value 3.1)
A.ResizeImagRow(1, 3);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

ClearRealRow

Syntax :

  void ClearRealRow(int i)

This method clears the real part of row i.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateRealRow(0, 3);
A.IndexReal(0, 0) = 0; A.ValueReal(0, 0) = 2.3;
A.IndexReal(0, 1) = 3; A.ValueReal(0, 1) = -0.8;
A.IndexReal(0, 2) = 7; A.ValueReal(0, 2) = 1.9;
// row 1 with 4 non-zero entries
A.ReallocateRealRow(1, 4);
A.IndexReal(1, 0) = 5; A.ValueReal(1, 0) = 3.1;
A.IndexReal(1, 1) = 1; A.ValueReal(1, 1) = -1.3;
A.IndexReal(1, 2) = 0; A.ValueReal(1, 2) = 2.4;
A.IndexReal(1, 3) = 2; A.ValueReal(1, 3) = 0.4;
// column numbers are not sorted -> AssembleRealRow
A.AssembleRealRow(1);

// removing all non-zero entries of row 0
A.ClearRealRow(0);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

ClearImagRow

Syntax :

  void ClearImagRow(int i)

This method clears the imaginary part of row i.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateImagRow(0, 3);
A.IndexImag(0, 0) = 0; A.ValueImag(0, 0) = 2.3;
A.IndexImag(0, 1) = 3; A.ValueImag(0, 1) = -0.8;
A.IndexImag(0, 2) = 7; A.ValueImag(0, 2) = 1.9;
// row 1 with 4 non-zero entries
A.ReallocateRealRow(1, 4);
A.IndexImag(1, 0) = 5; A.ValueImag(1, 0) = 3.1;
A.IndexImag(1, 1) = 1; A.ValueImag(1, 1) = -1.3;
A.IndexImag(1, 2) = 0; A.ValueImag(1, 2) = 2.4;
A.IndexImag(1, 3) = 2; A.ValueImag(1, 3) = 0.4;
// column numbers are not sorted -> AssembleImagRow
A.AssembleImagRow(1);

// removing all non-zero entries of row 0
A.ClearImagRow(0);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

SwapRealRow

Syntax :

  void SwapRealRow(int i, int j)

This method swaps the rows i and j (only real part), the columns numbers are unchanged. This method should be considered carefully for symmetric matrices, since the condition i <= j may be not satisfied anymore after swapping the rows.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateRealRow(0, 3);
A.IndexReal(0, 0) = 0; A.ValueReal(0, 0) = 2.3;
A.IndexReal(0, 1) = 3; A.ValueReal(0, 1) = -0.8;
A.IndexReal(0, 2) = 7; A.ValueReal(0, 2) = 1.9;
// row 1 with 4 non-zero entries
A.ReallocateRealRow(1, 4);
A.IndexReal(1, 0) = 5; A.ValueReal(1, 0) = 3.1;
A.IndexReal(1, 1) = 1; A.ValueReal(1, 1) = -1.3;
A.IndexReal(1, 2) = 0; A.ValueReal(1, 2) = 2.4;
A.IndexReal(1, 3) = 2; A.ValueReal(1, 3) = 0.4;
// column numbers are not sorted -> AssembleRealRow
A.AssembleRealRow(1);

// exchanging contents of row 0 and row 1
A.SwapRealRow(0, 1);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

SwapImagRow

Syntax :

  void SwapImagRow(int i, int j)

This method swaps the rows i and j (only imaginary part), the columns numbers are unchanged. This method should be considered carefully for symmetric matrices, since the condition i <= j may be not satisfied anymore after swapping the rows.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateImagRow(0, 3);
A.IndexImag(0, 0) = 0; A.ValueImag(0, 0) = 2.3;
A.IndexImag(0, 1) = 3; A.ValueImag(0, 1) = -0.8;
A.IndexImag(0, 2) = 7; A.ValueImag(0, 2) = 1.9;
// row 1 with 4 non-zero entries
A.ReallocateImagRow(1, 4);
A.IndexImag(1, 0) = 5; A.ValueImag(1, 0) = 3.1;
A.IndexImag(1, 1) = 1; A.ValueImag(1, 1) = -1.3;
A.IndexImag(1, 2) = 0; A.ValueImag(1, 2) = 2.4;
A.IndexImag(1, 3) = 2; A.ValueImag(1, 3) = 0.4;
// column numbers are not sorted -> AssembleImagRow
A.AssembleImagRow(1);

// exchanging contents of row 0 and row 1
A.SwapImagRow(0, 1);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

ReplaceRealIndexRow

Syntax :

  void ReplaceRealIndexRow(int i, Vector<int>& ind)

This method replaces column numbers of real part of row i. The size of array ind must be greater or equal to the size of the row i.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateRealRow(0, 3);
A.IndexReal(0, 0) = 0; A.ValueReal(0, 0) = 2.3;
A.IndexReal(0, 1) = 3; A.ValueReal(0, 1) = -0.8;
A.IndexReal(0, 2) = 7; A.ValueReal(0, 2) = 1.9;

// column numbers are not 0, 3, 7, but 1, 2, 6 =>
IVect new_col(3);
new_col(0) = 1;
new_col(1) = 2;
new_col(2) = 6;
A.ReplaceRealIndexRow(0, new_col);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

ReplaceImagIndexRow

Syntax :

  void ReplaceImagIndexRow(int i, Vector<int>& ind)

This method replaces column numbers of imaginary part of row i. The size of array ind must be greater or equal to the size of the row i.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateImagRow(0, 3);
A.IndexImag(0, 0) = 0; A.ValueImag(0, 0) = 2.3;
A.IndexImag(0, 1) = 3; A.ValueImag(0, 1) = -0.8;
A.IndexImag(0, 2) = 7; A.ValueImag(0, 2) = 1.9;

// column numbers are not 0, 3, 7, but 1, 2, 6 =>
IVect new_col(3);
new_col(0) = 1;
new_col(1) = 2;
new_col(2) = 6;
A.ReplaceImagIndexRow(0, new_col);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

GetRealRowSize

Syntax :

 int GetRealRowSize(int i) const

This method returns the number of non-zero entries contained in the real part of i-th row.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateRealRow(0, 3);
A.IndexReal(0, 0) = 0; A.ValueReal(0, 0) = 2.3;
A.IndexReal(0, 1) = 3; A.ValueReal(0, 1) = -0.8;
A.IndexReal(0, 2) = 7; A.ValueReal(0, 2) = 1.9;

// GetRealRowSize should return 3
cout << "Number of non-zero entries in row 0 : " << A.GetRealRowSize(0, 3) << endl;

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

GetImagRowSize

Syntax :

 int GetImagRowSize(int i) const

This method returns the number of non-zero entries contained in the imaginary part of i-th row.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateImagRow(0, 3);
A.IndexImag(0, 0) = 0; A.ValueImag(0, 0) = 2.3;
A.IndexImag(0, 1) = 3; A.ValueImag(0, 1) = -0.8;
A.IndexImag(0, 2) = 7; A.ValueImag(0, 2) = 1.9;

// GetImagRowSize should return 3
cout << "Number of non-zero entries in row 0 : " << A.GetImagRowSize(0, 3) << endl;

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

PrintRealRow

Syntax :

 void PrintRealRow(int i) const

This method displays the real part of i-th row.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// displaying row 3
cout << "Row 3 = " << endl;
A.PrintRealRow(3);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

PrintImagRow

Syntax :

 void PrintImagRow(int i) const

This method displays the imaginary part of i-th row.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// displaying row 3
cout << "Row 3 = " << endl;
A.PrintImagRow(3);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

AssembleRealRow

Syntax :

  void AssembleRealRow(int i)

This method sorts column numbers of real part of a row, and adds values if there are duplicate column numbers. This method is not necessary if you are using AddInteraction, AddInteractionRow, GetReal, GetImag or Set.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateRealRow(0, 3);
A.IndexReal(0, 0) = 0; A.ValueReal(0, 0) = 2.3;
A.IndexReal(0, 1) = 3; A.ValueReal(0, 1) = -0.8;
A.IndexReal(0, 2) = 7; A.ValueReal(0, 2) = 1.9;
// row 1 with 4 non-zero entries
A.ReallocateRealRow(1, 4);
A.IndexReal(1, 0) = 5; A.ValueReal(1, 0) = 3.1;
A.IndexReal(1, 1) = 1; A.ValueReal(1, 1) = -1.3;
A.IndexReal(1, 2) = 0; A.ValueReal(1, 2) = 2.4;
A.IndexReal(1, 3) = 2; A.ValueReal(1, 3) = 0.4;
// column numbers are not sorted -> AssembleRealRow
A.AssembleRealRow(1);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

AssembleImagRow

Syntax :

  void AssembleImagRow(int i)

This method sorts column numbers of imaginary part of a row, and adds values if there are duplicate column numbers. This method is not necessary if you are using AddInteraction, AddInteractionRow, GetReal, GetImag or Set.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// initializing row 0 with 3 non-zero entries :
A.ReallocateImagRow(0, 3);
A.IndexImag(0, 0) = 0; A.ValueImag(0, 0) = 2.3;
A.IndexImag(0, 1) = 3; A.ValueImag(0, 1) = -0.8;
A.IndexImag(0, 2) = 7; A.ValueImag(0, 2) = 1.9;
// row 1 with 4 non-zero entries
A.ReallocateImagRow(1, 4);
A.IndexImag(1, 0) = 5; A.ValueImag(1, 0) = 3.1;
A.IndexImag(1, 1) = 1; A.ValueImag(1, 1) = -1.3;
A.IndexImag(1, 2) = 0; A.ValueImag(1, 2) = 2.4;
A.IndexImag(1, 3) = 2; A.ValueImag(1, 3) = 0.4;
// column numbers are not sorted -> AssembleImagRow
A.AssembleImagRow(1);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

AddInteraction

Syntax :

  void AddInteraction(int i, int j, complex<T> val)

This method adds val to A(i, j). If there is no non-zero entry at this position, a new non-zero entry is created.

Example :

// initially the matrix is equal to 0 (empty)
Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// then you add values with AddInteraction
A.AddInteraction(0, 1, complex<double>(1.2, 0));
A.AddInteraction(1, 2, complex<double>(1.8, 0.2));
A.AddInteraction(3, 0, complex<double>(0, 0.5));
A.AddInteraction(4, 5, complex<double>(0, 1.6));
A.AddInteraction(6, 2, complex<double>(-2.0, 0.2));

// you can also use AddInteractionRow, if there are several values
// to add in the same time, these values may be not sorted
int nb_val = 4;
IVect col(nb_val);
Vector<complex<double> > values(nb_val);
col(0) = 0; values(0) = complex<double>(2.1, 0);
col(1) = 7; values(1) = complex<double>(0, 0.8);
col(2) = 3; values(2) = complex<double>(-2.6, 0);
col(3) = 2; values(3) = complex<double>(0.9, -3.4);

A.AddInteractionRow(6, nb_val, col, values);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

AddInteractionRow

Syntax :

  void AddInteractionRow(int i, int nb_values, const IVect col, const Vector<complex<T> > val)

This method adds nb_values values in row i. For each value to add, you provide the column number and the value.

Example :

// initially the matrix is equal to 0 (empty)
Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// then you add values with AddInteraction
A.AddInteraction(0, 1, complex<double>(1.2, 0));
A.AddInteraction(1, 2, complex<double>(1.8, 0.2));
A.AddInteraction(3, 0, complex<double>(0, 0.5));
A.AddInteraction(4, 5, complex<double>(0, 1.6));
A.AddInteraction(6, 2, complex<double>(-2.0, 0.2));

// you can also use AddInteractionRow, if there are several values
// to add in the same time, these values may be not sorted
int nb_val = 4;
IVect col(nb_val);
Vector<complex<double> > values(nb_val);
col(0) = 0; values(0) = complex<double>(2.1, 0);
col(1) = 7; values(1) = complex<double>(0, 0.8);
col(2) = 3; values(2) = complex<double>(-2.6, 0);
col(3) = 2; values(3) = complex<double>(0.9, -3.4);

A.AddInteractionRow(6, nb_val, col, values);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

AddInteractionColumn

Syntax :

  void AddInteractionColumn(int i, int nb_values, const IVect row, const Vector<complex<T> > val)

This method adds nb_values values in column i. For each value to add, you provide the row number and the value.

Example :

// initially the matrix is equal to 0 (empty)
Matrix<complex<double>, General, ArrayRowComplexSparse> A(12, 8);
// then you add values with AddInteraction
A.AddInteraction(0, 1, complex<double>(1.2, 0));
A.AddInteraction(1, 2, complex<double>(1.8, 0.2));
A.AddInteraction(3, 0, complex<double>(0, 0.5));
A.AddInteraction(4, 5, complex<double>(0, 1.6));
A.AddInteraction(6, 2, complex<double>(-2.0, 0.2));

// you can also use AddInteractionColumn, if there are several values
// to add in the same time, these values may be not sorted
int nb_val = 4;
IVect row(nb_val);
Vector<complex<double> > values(nb_val);
row(0) = 0; values(0) = complex<double>(2.1, 0);
row(1) = 7; values(1) = complex<double>(0, 0.8);
row(2) = 3; values(2) = complex<double>(-2.6, 0);
row(3) = 2; values(3) = complex<double>(0.9, -3.4);

A.AddInteractionColumn(5, nb_val, col, values);

Location :

Class Matrix_ArrayComplexSparse
Matrix_ArrayComplexSparse.hxx Matrix_ArrayComplexSparse.cxx

Print

Syntax :

  void Print()

This method displays the matrix.

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(4, 3);
cout << " A = " << endl;
A.Print();

Location :

Write

Syntax :

  void Write(string name)

This method writes the matrix on a file in binary format. This format is not portable, so if you read a matrix with method Read, the storage should be the same as the storage used when the matrix has been written.

Example :

// storage ArrayRowSymComplexSparse when writing
Matrix<complex<double>, General, ArrayRowSymComplexSparse> A(8, 8);
A.Write("MyMatrix.dat");

// same storage when reading the matrix
Matrix<complex<double>, General, ArrayRowSymComplexSparse> B;
B.Read("MyMatrix.dat");

Location :

Read

Syntax :

  void Read(string name)

This method reads the matrix from a file in binary format. This format is not portable, so if you read a matrix with method Read, the storage should be the same as the storage used when the matrix has been written.

Example :

// storage ArrayRowSymComplexSparse when writing
Matrix<complex<double>, General, ArrayRowSymComplexSparse> A(8, 8);
A.Write("MyMatrix.dat");

// same storage when reading the matrix
Matrix<complex<double>, General, ArrayRowSymComplexSparse> B;
B.Read("MyMatrix.dat");

Location :

WriteText

Syntax :

  void WriteText(string name)
  void WriteText(string name, bool without_brackets)
  void WriteText(ostream out)
  void WriteText(ostream out, bool without_brackets)

This method writes the matrix on a file in ascii format. The row and column numbers are incremented in order to satisfy the 1-index convention (used by Matlab). The complex values are written by default with parenthesis. The file will look like

1 3 (0.5432143,-2.34433)
2 4 (2.90843,0.0)
3 2 (-1.232409,-0.090982)

If you prefer to not have those brackets, but real part and imaginary part in separated columns, you have to put true in the optional argument. In that case, the file will be :

1 3 0.5432143 -2.34433
2 4 2.90843 0.0
3 2 -1.232409 -0.090982

The Matlab code would be in that last case :

M = load('matrix.dat');
A = spconvert(M(:,1:3)) + 1i*spconvert(M(:,[1,2,4]));

With Python, it is similar :

from scipy.sparse import *

A = loadtxt('matrix.dat')
B = coo_matrix((A[:,2],(A[:,0]-1,A[:,1]-1))) + 1j*coo_matrix((A[:,3],(A[:,0]-1,A[:,1]-1)))

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A(8, 8);
// filling the matrix
A.AddInteraction(0, 3, complex<double>(0.3, 1.2));
// ...

// then writing on the disk
A.WriteText("my_matrix.dat");

Location :

ReadText

Syntax :

  void ReadText(string name)
  void ReadText(string name, bool without_brackets)
  void ReadText(istream in)
  void ReadText(istream in, bool without_brackets)

This method reads the matrix from a file in ascii format. The row and column numbers on the file should be based on the 1-index convention (used by Matlab). The complex values are expected to be by default with parenthesis. The file would look like (row numbers are placed on the first column, column numbers in the second column, and values and the third column)

1 3 (0.5432143,-2.34433)
2 4 (2.90843,0.0)
3 2 (-1.232409,-0.090982)

If your file is written without those brackets, but real part and imaginary part in separated columns, you have to put true in the optional argument. In that case, the file should be :

1 3 0.5432143 -2.34433
2 4 2.90843 0.0
3 2 -1.232409 -0.090982

Example :

Matrix<complex<double>, General, ArrayRowComplexSparse> A;
// you can read A from a file
A.ReadText("my_matrix.dat");

Basic declaration of easily modifiable sparse complex matrices:

Classes :

Example :

Methods for easily modifiable sparse complex matrices :

Basic declaration of Harwell-Boeing sparse matrices:

Classes :

Example :

Methods for Harwell-Boeing sparse matrices :

Matrix constructors for ArrayRowComplexSparse, ArrayRowSymComplexSparse

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Example :

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Matrix constructors for RowComplexSparse, RowSymComplexSparse

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Example :

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Matrix operators

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Example :

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GetM

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GetN

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GetDataSize, GetNonZeros

Syntax :

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GetMemorySize

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GetRealDataSize,GetRealNonZeros

Syntax :

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GetImagDataSize, GetImagNonZeros

Syntax :

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GetRealData for ArrayRowComplexSparse, ArrayRowSymComplexSparse

Syntax :

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GetImagData for ArrayRowComplexSparse, ArrayRowSymComplexSparse

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GetRealData for RowComplexSparse, RowSymComplexSparse

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GetImagData for RowComplexSparse, RowSymComplexSparse

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GetRealInd for RowComplexSparse, RowSymComplexSparse

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GetImagInd for RowComplexSparse, RowSymComplexSparse

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